Heat oil in a large soup pot over medium-high heat. Add sausage and shallots then saute until sausage begins to brown, 3-4 minutes. Add sweet corn then saute for 2 minutes. Sprinkle in 2-1/2 teaspoons Old Bay seasoning then saute for 30 more seconds.
Add chicken broth then turn heat up to high and bring to a boil. Add potatoes then turn heat down to medium and simmer until potatoes are tender, 10-15 minutes. Add shrimp then remove pot from heat, place a lid on top, and let shrimp cook through, 3-4 minutes. Taste then add up to 1/2 teaspoon more Old Bay if needed then ladle into bowls and serve with lemon wedges.
Notes
If you are sensitive to spice, swap andouille sausage for mild kielbasa sausage.
This soup is great served over a scoop of cooked white rice.